The representation of measurement signals or signal vectors measured by multi-channel measuring devices in some natural signal space basis is useful from the point of view of the analysis and illustration of the measured phenomenon. For example, in the case of a multi-channel magnetometer, one such basis can be obtained by modeling the source that produced the magnetic field by a current distribution whose total amplitude is the smallest possible one among the distributions that are capable of producing the measured signal vector and which current distribution has been limited within a conductor area that describes the object to be examined. This kind of method is called a minimum norm estimate and it has been described e.g. in publication “Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain”, Matti Hämäläinen et al Reviews of Modern Physics, Vol. 65, No. 2, 1993. In practice, due to the numerical sensitivity, the modeling of signal vectors by minimum norm estimate requires regularisation whose intensity depends, for each case specifically, on the signal-to-noise ratio and on the distribution of the vector field often in a non-obvious manner. Thus, the use of minimum norm estimate requires consideration and good expertise because a wrong regularisation may lead to a completely erroneous modeling. Another problem associated with the minimum norm estimate is that it tends to model also external interferences in the source distribution of an object to be examined, which leads to an erroneous outcome. In addition, the minimum norm estimate is a rather laborious operation computationally.
The source distribution that produced the vector field has also been modelled by means of a multi-pole development, but in that case, the source model has usually not been formed to be the basis for signal space. At a theoretical level, the formation of a basis based on a multi-pole development has been presented in the doctoral thesis “Interpretation of Neuromagnetic Measurements: Modeling and Statistical Considerations”, Matti Hämäläinen, 1987, in which the basis is designed to describe the magnetic field outside an area containing the source distribution. The multi-pole development has also been used for source modeling in magnetocardiography, but in that case one has not formed a basis for signal space of the development. This is apparent e.g. from the publication “Comparability of Measurement Results Obtained with Multi-SQUID-Systems of Different Sensor Configurations”, M. Burghoff et al, IEEE Transactions on Applied Superconductivity, Vol. 7, No. 2, 1997. The formation of the basis for signal space based on the series development of the vector field is reasonable only if the measuring device is a sufficiently multi-channel one and appropriate with respect to its geometry to ensure a susceptibility to interference as small as possible.
External interferences e.g. from the magnetic fields caused by the electric conductors situated near the measurement space are easily summed up in subtle magnetometer measurements. The elimination of the external interferences from the measured signals is important in order that one could obtain information as dependable as possible from the object to be examined. Conventionally, as the interference elimination methods, projection and reference signals methods have been used. In the former method, the interference elimination is based upon information on signal subspace spanned by known interferences, and in the latter one upon signals measured by correctly placed reference sensors, which signals are assumed to hive been caused merely by interference sources.
Of projection methods let it be mentioned the SSP projection method in which the sub-space caused by typical external interference sources is determined and the measured signals are projected against this orthogonally to the space. In addition to the interference, the projection also diminishes the actual interesting signal, in case the signal vectors produced by the object to be examined are not orthogonal to the interference sub-space, and furthermore, the SSP eliminates the interference completely only in cases in which the external interferences really belong to a predetermined interference sub-space. Also the illustration of the spatial distribution of the signals suffers from the projection. The SSP method has been described e.g. in patent publication F1925461 and in publication “Signal-space projection method for separating MEG or EEG into components”, M. A. Uusitalo and R. J. Ilmoniemi, Medical & Biological Engineering & Computing, Vol. 35, pp. 135-140, 1997.
In reference signal methods, so-called reference sensors are installed in the measuring device in such places with respect to other sensors that they can be considered to measure solely external interferences without observing any signal from the object to be measured. Taking into account the geometry between the reference and the actual signal channels, the signals associated with the external interferences can be calculated and reduced from the signals measured by the signal channels, in which case just the signal relating to the object to be measured is remaining. This kind of method is justified only when the reference sensors are capable of measuring all the information relating to the external interferences in the area of the signal sensors without, however, measuring the signal associated with the object at all. In other words, the method is based on an assumption according to which external interferences in the area of the measuring device are uniform, whereas the signals produced by the object to be measured are weakening very fast as the distance grows. The method based on the reference signals is described e.g. in patent publication WO9641209.
In addition to external interferences, one problem that distorts the signals is the possible movement of the object to be examined during the measurement. Lately, e.g. in magnetoencephalography there have been made excitation response measurements to testees who cannot keep their heads immovable during the measurement. An apparent solution is to reject from the signals to be averaged signals that correspond to such moments of time during which the head has been situated too far from some reference point. In this kind of method, the signal-to-noise ratio weakens due to the rejection of the responses particularly when the head moves much. In more advanced methods, the distortion caused by a movement can be corrected either by taking the into account the movement in the source modeling when using a distorted averaged signal, or by making the movement correction directly to the signals prior to averaging these. The latter method is better in that sense that as the outcome, a signal vector in an illustrative form is obtained. For this purpose, minimum norm estimate is used by determining the source distribution associated with every response to be averaged and by calculating from this a signal corresponding to some fixed location of head. The problem with the method is the computational slowness of the minimum norm estimate, the distorting effect of the external interferences, and the fact that the possibly great distance of the object to the measurement sensors may distort the result. Methods of correcting movements have been described e.g. in the publication “Detecting and Correcting for Head Movements in Neuromagnetic Measurements”, K. Uutela et al, NeuroImage, Vol. 14, pp. 1424-1431, 2001.
The transformation of signal vectors from one measurement geometry to another is often necessary e.g. when comparing different measurements with one another. The question can be e.g. about the transformation of each measured signal vector into a signal vector of such a measuring device in which the measurement sensors are situated in determinate positions on the surface of some standard object. To calculate such virtual signals, the vector field must be divided into basis function components, based on which the virtual signals can be calculated by forming the basis of the vector field for the virtual set of sensors and by using estimated components to calculate the virtual signals. Conventionally, as the basis, a minimum norm estimate basis has been used, in which case the aforementioned regularisation and interference problems hamper the outcome. The use of the minimum norm estimate for calculating virtual signals has been described e.g. in the publication “Transformation of Multichannel Magnetocardiographic Signals to Standard Grid Form”, Jussi Numminen et al, IEEE Transactions on Biomedical Engineering, Vol. 42, No. 1, 1995.
The modeling of the sources that produced the measured signal is typically implemented by parametrising the source model and by calculating the parameters e.g. by non-linear minimisation of the smallest square sum of the error in such a manner that the model and the measured signal correspond to each other as well as possible. In that case, in the minimisation algorithm one must perform the calculation of the parameterised model for each measurement sensor specifically, which results in a big number of arithmetic operations when the number of sensors is big. One further problem is the difficulty of setting a good initial guesstimate for the model that would fasten the convergence of the minimisation algorithm towards the correct solution.
The inaccuracy of the information concerning the calibration coefficients and the geometry of the measuring device causes errors when analysing an object to be examined. In this sense the measuring device must be checked so that the measured signal vectors are compared to some expected result, in which case the calibration coefficients and the geometric parameters can be so set that the possible deviation from the expected result vanishes. Conventionally, in calibration methods one has used an exactly known signal source which is situated in a known position with respect to the measuring device. The problem with the method is that one must rely on the ideality of the signal source. Furthermore, calibration measurements of this kind often are cumbersome and time-consuming to perform.